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Block #726,334

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/17/2014, 8:40:34 PM Β· Difficulty 10.9610 Β· 6,071,267 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
2695671c74ad0342b6809d9635a2437b386a3c0a967ae048d092e5519266762b
View on Chainz β†—

Height

#726,334

Difficulty

10.961002

Transactions

1

Size

243 B

Version

2

Bits

0af6043b

Nonce

682,272,250

Timestamp

9/17/2014, 8:40:34 PM

Confirmations

6,071,267

Merkle Root

880d926a45cb35a014feaa6b548fab512f7fccae24f7dd0151752be80cf479c7
Transactions (1)
Coinbase880d926a45cb35…752be80cf479c7
1 in β†’ 2 out8.3100 XPM152 B
AVsg8K1F…ZPDrnoURALPu3s2c…EJXLjVFh
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

8.475 Γ— 10⁹⁡(96-digit number)
84756446748969220822…65755568111800597160
Discovered Prime Numbers
p_k = 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
8.475 Γ— 10⁹⁡(96-digit number)
84756446748969220822…65755568111800597161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.695 Γ— 10⁹⁢(97-digit number)
16951289349793844164…31511136223601194321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.390 Γ— 10⁹⁢(97-digit number)
33902578699587688328…63022272447202388641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.780 Γ— 10⁹⁢(97-digit number)
67805157399175376657…26044544894404777281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.356 Γ— 10⁹⁷(98-digit number)
13561031479835075331…52089089788809554561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.712 Γ— 10⁹⁷(98-digit number)
27122062959670150663…04178179577619109121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.424 Γ— 10⁹⁷(98-digit number)
54244125919340301326…08356359155238218241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.084 Γ— 10⁹⁸(99-digit number)
10848825183868060265…16712718310476436481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.169 Γ— 10⁹⁸(99-digit number)
21697650367736120530…33425436620952872961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.339 Γ— 10⁹⁸(99-digit number)
43395300735472241061…66850873241905745921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.679 Γ— 10⁹⁸(99-digit number)
86790601470944482122…33701746483811491841
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 726334

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock 2695671c74ad0342b6809d9635a2437b386a3c0a967ae048d092e5519266762b

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #726,334 on Chainz β†—
Circulating Supply:57,624,789 XPMΒ·at block #6,797,600 Β· updates every 60s
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